Normalized solutions for a Choquard equation with exponential growth in ${\mathbb{R}}^2$

In this paper, we study the existence of normalized solutions to the following nonlinear Choquard equation with exponential growth \begin{align*} \left{ \begin{aligned} &-Δu+λu=(I_α\ast F(u))f(u), \quad \quad \hbox{in }$\mathbb{R}$^{2},\ &\int_{$\mathbb{R}$^{2}}|u|^{2}dx=a^{2}, \end{aligned} \right. \end{align*} where $a>0$ is prescribed, $\lambda \in \mathbb{R}$, $\alpha \in (0,2)$, $I_{\alpha }$ denotes the Riesz potential, $\ast$ indicates the convolution operator, the function $f(t)$ has exponential growth in ${\mathbb{R}}^2$ and $F(t)={\int }_0^{t}f(\tau )d\tau$. Using the Pohozaev manifold and variational methods, we establish the existence of normalized solutions to the above problem.